Bi-planar coil assemblies for producing specified magnetic fields
a technology of biplanar coils and magnetic fields, applied in the direction of instruments, using reradiation, diagnostic recording/measuring, etc., can solve the problems of inability to yield a solution, affecting the design of complex magnetic fields, and affecting the quality of governing equations, etc., to achieve the effect of reducing the magnitude of the magnetic field
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example 1
5.1 Example 1
[0191]The T00 (Constant Field) Bi-pChecklanar Coil
[0192]In this example, the method of the invention is used to design shielded and unshielded bi-planar coils that are intended to produce symmetrically located T00 fields within the primary bi-planar coil. For this coil, the target fields are simply constants, and so HX is simply a constant on each of the three pairs of target planes. We therefore set
HTX(c1;y,z)=Hmax
HTX(c2;y,z)=Hmax
HTX(c3;y,z)=0. (5.2)
Here, the constant transverse magnetic field within the primary coils has been assumed to take the value Hmax=1 amp / meter. The target field at x=±c3 is set to zero, reflecting the intended function of the shields. Since the T00 field is even in the x-coordinate (it is constant), the primary coil windings on the plane at x=−a are in phase with those on x=a, and the same is true for the shields on the planes x=±b. (This even target field requires the last term in equation (4.11) to take a plus sign).
[0193]To begin, the cas...
example 2
5.2 Example 2
[0201]The T11 Bi-planar Coil
[0202]As a further illustration of the use of this invention, shielded bi-planar coils will be designed in this section, both for symmetric and asymmetrically located T11 fields. The transverse magnetic field component for this case has the general form HX(x,y,z)=C11x with C11 an arbitrary constant. It follows that the target fields on the three pairs of target planes used in this invention must be given by the equations
[0203]HTX(c1;y,z)=Hmax(c1a)HTX(c2;y,z)=Hmax(c2a)HTX(c3;y,z)=0.(5.3)
Here, the constant Hmax is now the maximum magnetic field strength (in the x-component) on the plane x=a of the primary coil. Its value is set to 1 amp / meter here, for illustrative purposes. As this target field is now anti-symmetric in x, it follows that the coils on the opposing planes of the bi-planar coil (and also the shields) are counter-wound. This is the case discussed explicitly in Section 4.3.
[0204]The primary winding for a shielded T11 coil ...
example 3
5.3 Example 3
[0211]The T21 Bi-planar Coil
[0212]Another illustration of the use of this invention concerns the design of shielded bi-planar T21 coils. The technique has been used to design both symmetric and asymmetrically located fields, although only the latter case will be discussed here.
[0213]The transverse component for a symmetrically located T21 magnetic field has the general form HX(x,y,z)=3C21xz, where C21 is again an arbitrary constant. For a field that is asymmetrically positioned with respect to the origin, it therefore follows that the target fields take the forms
[0214]HTX(c1;y,z)=Hmax(2c1a)Z2(q-p)HTX(c2;y,z)=Hmax(2c2a)Z2(q-p)HTX(c3;y,z)=0.(5.4)
[0215]Again, the constant Hmax is set to the value 1 amp / meter here, for illustrative purposes. This field (5.4) is also anti-symmetric in x, as for the case discussed in Section 5.2, and so the coils on the opposing planes of the bi-planar coil and shield are also counter-wound. The quantity Z2 in equations (5.4) is the ...
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